This concerns some noteworthy general properties of solutions. Assume that the coefficients p and q of the ODE (1) are continuous on some open interval I, to which the subsequent statements refer.(a) Solve y" ?? y = 0 (a) by exponential functions, (b) By hyperbolic functions. How are the constants in the corresponding general solution related?(b) Probe that the solutions of a basis cannot be 0 at the same point.(c) Probe that the solutions of a basis cannot have a maximum or minimum at the same point.(d) Express (y2/y1)' by a formula involving the Wronskian W. Why is it likely that such a formula should exist? Use it to find W in Prob. 10.(e) Sketch y1(x) = x3 if x > 0 and 0 if x 0 and x3 if x (f) Prove Abel??s formula6 where c = W (y1(x0), y2(x0)). Apply it to Prob.12.

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W(y₁(x), ₂(x)) = c exp -pa Хо p(t) dt